The talk addresses a philosophical comparison and thus interpretation of both theorems having one and the same subject: the absence of the other half of variables, called “hidden” for that, to the analogical set of variables in classical mechanics This implies the existence of quantum correlations, which can
exceed any classical correlations (e.g., violating Bell’s inequalities), thus quantum information and is essential for the interpretation of quantum mechanics. The theorem and proof of John von Neumann (1932) are formulated in the context of his fundamental treatise devoted to quantum mechanics (Mathematische Grundlagen der Quantenmechanik, pp. 167–173). He deduced the absence of hidden variables from the
availability of non-commuting operators in Hilbert space corresponding to conjugate physical variables in quantum mechanics. The unification of wave mechanics (1926) and matrix mechanics (1925) as well as of the representation by Ψ-functions (1930) implies the introduction of Hilbert space. The theorem of Simon Kochen and Ernst Specker (The problem of Hidden Variables in Quantum Mechanics, 1968) generalizes von
Neumann’s result: Once Hilbert space has introduced, this implies immediately the absence of hidden variables even if the quantities are non-conjugate and thus their corresponding selfadjoint operators in Hilbert space commute. The proof of Kochen and Specker is founded on the interpretation of the commeasurable quantities in quantum mechanics as mathematically commeasurable sets sharing a common measure
It introduces implicitly quantum measure unifying quantum leaps and smooth changes thus deducing entanglement and the absence of hidden variables from the core principle of quantum mechanics: wave-particle duality.